node2vec: Scalable Feature Learning for Networks
Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2016 · paper · AI and machine learning
Proposes node2vec, which learns low-dimensional representations of network nodes using a biased random walk that flexibly explores different kinds of neighborhoods. It reports gains over existing methods on multi-label classification and link prediction across several real-world networks.
Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.
4 findings
Reference or label Sec 4.4 prints "improves as the in-out parameter p and the return parameter q decrease", but Sec 3.2.2 defines "Return parameter, p" and "In-out parameter, q"; the names are swapped.
- p. 7 Section 4.4, second paragraph
improves as the in-out parameter p and the return parameter q decrease
- p. 4 Section 3.2.2 definitions
Return parameter, p.
- p. 4 Section 3.2.2 definitions
In-out parameter, q.
- p. 7
The performance of node2vec improves as the in-out parameter p and the return parameter q decrease.
Judge's note: Read the sentence on the page 7 image; the page 4 definitions were confirmed in the text layer only. The next sentence in 4.4 ("a low q encourages outward exploration, it is balanced by a low p") uses the Section 3 roles, so this is a label swap in one sentence and not a redefinition.
Second check: another model agreed
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Reference or label Reference [9] is printed as "Z. S. Harris. Word. Distributional Structure, 10(23):146–162, 1954.", with "Word" in the title position and "Distributional Structure" italicised as the venue; title and journal appear transposed, and "10(23)" looks like a collapsed "10(2-3)".
- p. 10 Reference [9]
Z. S. Harris. Word. Distributional Structure, 10(23):146–162, 1954.
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that Harris's 1954 article is titled "Distributional structure" and appeared in the journal Word, volume 10, issue 2-3. The page 10 crop confirms the entry as quoted: "Word." in roman type where the title goes and "Distributional Structure" in italics where the venue goes, followed by "10(23):146–162, 1954". The files cannot confirm the true bibliographic details.
Second check: another model agreed
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Wording Sec 4.7 says "node2vec outperforms both DeepWalk and LINE in all networks" for the best operator per algorithm, but Table 4 gives DeepWalk and node2vec the same best Facebook AUC, 0.9680 (Hadamard), both in bold.
- p. 9 Section 4.7, Experimental results, second paragraph
node2vec outperforms both DeepWalk and LINE in all networks
- p. 9 Table 4, block (b) Hadamard, Facebook column
0.9680
- p. 9 Section 4.7, Experimental results, second paragraph
node2vec outperforms both DeepWalk and LINE in all networks with gain up to 3.8% and 6.5% respectively
Judge's note: Viewed Table 4 on the page 9 image. In block (b), Facebook, DeepWalk is 0.9680 and node2vec is 0.9680, both bolded; DeepWalk's other operators are lower (0.7238, 0.9574, 0.9584). On Facebook the best-operator comparison is a tie at the printed precision, so "outperforms ... in all networks" overstates the table.
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Wording Section 4.7 says "node2vec outperforms DeepWalk and LINE barring a couple of cases involving the Weighted-L1 and Weighted-L2 operators in which LINE performs better", but Table 4 shows LINE above node2vec in four cells (PPI and arXiv under both operators), and DeepWalk ties node2vec at 0.9680 on Facebook under Hadamard.
- p. 9 Section 4.7, Experimental results, second paragraph
barring a couple of cases involving the Weighted-L1 and Weighted-L2 operators in which LINE performs better
- p. 9 Table 4, blocks (c) and (d), PPI and arXiv columns
0.7024
Only the authors can say what is right here.
Judge's note: Read Table 4 on the page 9 image. Block (c) Weighted-L1: PPI LINE 0.7024 vs node2vec 0.6292; arXiv LINE 0.8809 vs 0.8468. Block (d) Weighted-L2: PPI LINE 0.7106 vs 0.6236; arXiv LINE 0.8862 vs 0.8477. That is four operator/dataset cells, not two. Block (b) Hadamard, Facebook: DeepWalk 0.9680 and node2vec 0.9680, both bold, so a tie rather than outperformance. No explanation elsewhere in the text. "A couple" may be meant loosely (two operators or two datasets), so this is a wording issue for the authors. The sentence also cites "Table 1" for the operators, which is correct, since Table 1 defines them.
Second check: another model agreed
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21 minor (typos and the like; most checked by the judge only)
Wording Inconsistent term: "DeepWalk uses hierarchical sampling to approximate the softmax probabilities" is followed immediately by "However, hierarchical softmax is inefficient when compared with negative sampling"; "hierarchical softmax" appears to be meant in both.
- p. 6 Section 4.2, paragraph on equal sampling budget
DeepWalk uses hierarchical sampling to approximate the softmax probabilities
Judge's note: Viewed page 6 image, left column, last paragraph. The two adjacent sentences name the same technique differently, and the second sentence shows the intended term. This is a wording slip, not a factual error. The "one use by" slip in the same sentence is handled in C013.
Second check: another model agreed
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Wording Sec 4.7 prints "gain up to 3.8% and 6.5% respectively" over DeepWalk and LINE; from Table 4 the largest best-operator gain over DeepWalk (PPI, 0.7719 vs 0.7441) is 3.7%.
- p. 9 Section 4.7, Experimental results, second paragraph
with gain up to 3.8% and
- p. 9 Table 4, block (b), PPI column
0.7719
- p. 9 Section 4.7, Experimental results, second paragraph
gain up to 3.8% and 6.5% respectively
- p. 9 Table 4, block (b), PPI column
0.7441
Only the authors can say what is right here.
Judge's note: Viewed Table 4 on the page 9 image. Best-operator gains over DeepWalk are 3.74% on PPI, 0% on Facebook and 0.28% on arXiv. Even at the extremes of the rounding intervals the PPI ratio is about 1.037497, just short of 3.75%, so 3.8% is not reachable from the printed values. The 6.5% LINE figure does reproduce. The difference is 0.1 point, possibly from different unrounded runs.
Second check: another model agreed
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Typo Misspelling across a line break: "akin to backpro-pogation on just single hidden-layer feedforward neural networks" should read "backpropagation".
- p. 1 Introduction, last paragraph on the page
akin to backpro-
Judge's note: Viewed page 1 image, right column, last paragraph: the line ends "backpro-" and the next begins "pogation". The text layer agrees. The misspelling is in the second half of the word, not caused by the hyphenation.
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Typo Misspelling: "The word feature representations are learned by optmizing the likelihood objective" should read "optimizing".
- p. 3 Section 2, top of left column
learned by optmizing
- p. 3 Sec 2
optmizing
Judge's note: Viewed page 3 image, top of left column; "optmizing" is printed, and the text layer agrees.
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Typo Misspelling: "the mapping function from nodes to feature representaions we aim to learn" should read "representations".
- p. 3 Section 3, first paragraph
feature representaions
Judge's note: Viewed page 3 image, Section 3, first paragraph; "representaions" is printed, and the text layer agrees.
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Typo Grammar: "turn a network into a ordered sequence of nodes" should read "an ordered sequence".
- p. 3 Section 2, second paragraph on the page
turn a network into a ordered sequence
- p. 3 Sec 2
into a ordered sequence of
Judge's note: Viewed page 3 image, Section 2, second paragraph on the page; "into a ordered sequence" is printed, and the text layer agrees.
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Typo Wrong word form: "This is hard given we have a constrain on the sample size" should read "a constraint".
- p. 4 Section 3.1, DFS paragraph
we have a constrain on the sample size
Judge's note: Viewed page 4 image, Section 3.1, DFS paragraph; "a constrain on the sample size" is printed, and the text layer agrees.
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Typo Missing word: "the distribution of 1-hop nodes with respect the source node" should read "with respect to the source node".
- p. 4 Section 3.1, top of left column
with respect the source node
Judge's note: Viewed page 4 image, left column, first paragraph; "with respect the source node" is printed, and the text layer agrees.
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Typo Misspelling: "a function of the preceeding node in the walk t" should read "preceding".
- p. 4 Section 3.2.2, In-out parameter paragraph
a function of the preceeding node
- p. 4 Sec 3.2.2
preceeding node
- p. 4
the preceeding node in the walk t
Judge's note: Viewed page 4 image, right column, in-out parameter paragraph; "preceeding" is printed, and the text layer agrees.
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Typo Misspelling in Algorithm 1 (node2vecWalk): "Inititalize walk to [u]" should read "Initialize".
- p. 5 Algorithm 1, node2vecWalk
Inititalize walk to [u]
Judge's note: Viewed page 5 image, Algorithm 1; "Inititalize walk to [u]" is printed, while "Initialize walks to Empty" is spelled correctly earlier in the same algorithm.
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Typo Grammar: "an objective similar to the one use by node2vec" should read "the one used by".
- p. 6 Section 4.2, paragraph on equal sampling budget
similar to the one use by node2vec
Judge's note: Viewed page 6 image, left column, last paragraph; "the one use by node2vec" is printed, and the text layer agrees.
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Typo Misspellings: "The word cooccurence network is fairly dense, since edges exist between words cooccuring in a 2-length window" should read "cooccurrence" and "cooccurring".
- p. 6 Sec 4.3
cooccurence network
- p. 6 Sec 4.3
cooccuring
Judge's note: Viewed page 6 image, right column, Section 4.3 last paragraph; both misspellings are printed and the text layer agrees. The same page spells "cooccurrence" correctly in the Table 2 caption and the Wikipedia bullet.
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Typo Missing space between sentences: "with a p-value of less than 0.01.The best in-out and return hyperparameters were learned".
- p. 6 Sec 4.2
less than 0.01.The best
Judge's note: Viewed page 6 image, right column, Section 4.2; "0.01.The" is set with no space after the full stop, and the text layer shows the same, so it is not an extraction artefact.
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Typo Sec 4.3 prints "From the results, it is evident we can see how the added flexibility": two alternative phrasings are fused.
- p. 7 Section 4.3, Experimental results, second paragraph
From the results, it is evident we can see how the added flexi-
- p. 7 Sec 4.3
it is evident we can see how
Judge's note: Seen on the page 7 image as quoted. Either "it is evident how" or "we can see how" was intended.
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Typo Sec 4.3 prints "avoiding redudancy"; it should read "redundancy".
- p. 7 Section 4.3, Experimental results, second paragraph
avoiding redudancy
- p. 7 Sec 4.3
redudancy
Judge's note: Misspelling seen on the page 7 image and in the text layer.
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Typo Sec 4.5 prints "we measure per-formace as a function of the fraction of missing edges"; it should read "performance".
- p. 8 Section 4.5, first paragraph
we measure per-
Judge's note: Seen on the page 8 image: the word breaks across a line as "per-" / "formace", with the "n" missing.
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Typo Sec 4.7 prints "achieving the best AUC improvement on 12.6% on the arXiv dataset"; it should read "improvement of 12.6%".
- p. 9 Section 4.7, Experimental results, first paragraph
best AUC improvement on 12.6% on the arXiv dataset
- p. 9 Section 4.7, Experimental results, first paragraph
achieving the best AUC im-provement on 12.6% on the arXiv dataset
- p. 9 Sec 4.7
achieving the best AUC im-provement on 12.6%
Judge's note: Wrong preposition seen on the page 9 image. The number itself reproduces from Table 4 (node2vec 0.9366 vs Adamic-Adar 0.8315 on arXiv).
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Typo Table 4 caption prints "embedding based methods boot-stapped using binary operators"; it should read "bootstrapped".
- p. 9 Table 4 caption
embedding based methods boot-
Judge's note: Seen in the Table 4 caption on the page 9 image: the word breaks as "boot-" / "stapped", with the "r" missing.
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Typo Sec 4.7 prints "Since none of feature learning algorithms have been previously used for link prediction"; the article "the" is missing.
- p. 9 Section 4.7, second paragraph
Since none of feature learning algorithms have been previously
Judge's note: Seen on the page 9 image as quoted.
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Typo Table 4 caption reads "embedding based methods boot-stapped using binary operators"; the word should be "bootstrapped" (missing "r").
- p. 9 Table 4 caption
boot-stapped
Judge's note: The page 9 image and crop show the caption breaking as "boot-" / "stapped", which joins to "bootstapped". Section 3.3 of the text uses "bootstrapping". This is a real misspelling, not a hyphenation or extraction artefact.
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Typo Reference [25] lists "C. Funk, Verspoor, et al."; the author "Verspoor" has no initials, unlike every other author in the entry.
- p. 10 Reference [25]
C. Funk, Verspoor, et al.
Judge's note: The page 10 crop shows "T. Wittkop, A. Sokolov, K. Graim, C. Funk, Verspoor, et al." All other authors in the entry carry initials. The missing initial itself cannot be supplied from the files.
Second check: none (judge only)